Question

What is the molarity of a solution containing \(15.6 \mathrm{~g}\) of \(\mathrm{KCl}\) in \(274 \mathrm{~mL}\) of \(\mathrm{KCl}\) solution?

Short answer

The molarity of the solution is \(0.763 \text{ M}\).

Step-by-step solution

Calculate the molar mass of \(\text{KCl}\)

To find the molar mass of \(\text{KCl}\), add the atomic masses of potassium (K) and chlorine (Cl). The atomic mass of K is approximately \(39.1 \text{ g/mol}\) and the atomic mass of Cl is approximately \(35.45 \text{ g/mol}\). \[ \text{Molar mass of KCl} = 39.1 \text{ g/mol} + 35.45 \text{ g/mol} = 74.55 \text{ g/mol} \]

Convert grams of \(\text{KCl}\) to moles

Use the molar mass to convert the given mass of \(\text{KCl}\) to moles. \[ \text{Moles of KCl} = \frac{15.6 \text{ g}}{74.55 \text{ g/mol}} \] Let’s calculate the conversion: \[ \text{Moles of KCl} = 0.209 \text{ mol} \]

Convert volume from mL to L

Molarity is expressed in moles per liter, so convert the volume from \(\text{mL}\) to \(\text{L}\). There are \(1000 \text{ mL}\) in \(1 \text{ L}\). \[ \text{Volume in liters} = \frac{274 \text{ mL}}{1000} = 0.274 \text{ L} \]

Calculate the molarity

Molarity \(M\) is the number of moles of solute divided by the volume of solution in liters. \[ M = \frac{\text{moles of KCl}}{\text{volume in L}} = \frac{0.209 \text{ mol}}{0.274 \text{ L}} = 0.763 \text{ M} \]

Key concepts

Molar Mass

Understanding molar mass is key in solving many chemistry problems. The molar mass of a compound is the mass of one mole of that substance. It's found by adding up the atomic masses of all the atoms in a molecule. To find the molar mass, check the periodic table for the atomic masses of the elements you're dealing with. For example, in potassium chloride (KCl), you need the atomic masses of potassium (K) and chlorine (Cl).

• Potassium (K) has an atomic mass of approximately 39.1 g/mol.
• Chlorine (Cl) has an atomic mass of approximately 35.45 g/mol.

Add these values together to get the molar mass of KCl: \[ 39.1\text{ g/mol} + 35.45\text{ g/mol} = 74.55\text{ g/mol}\]This means one mole of KCl weighs 74.55 grams.

Moles to Grams Conversion

Converting between grams and moles is essential for molarity calculations. To convert grams to moles, you need the molar mass of the substance. The conversion formula is:\[ \text{Moles} = \frac{\text{Mass in grams}}{\text{Molar mass}}\]Say you have 15.6 grams of KCl. To find out how many moles this is, use the molar mass of KCl, which is 74.55 g/mol:\[ \frac{15.6 \text{ g}}{74.55 \text{ g/mol}} = 0.209 \text{ mol}\]So, 15.6 grams of KCl is equivalent to 0.209 moles.

Volume Conversion

Volume conversion is another vital step in calculating molarity. Molarity is expressed as moles per liter, so you'll often need to convert milliliters (mL) to liters (L). Remember, there are 1000 milliliters in one liter:\[ \text{Volume in liters} = \frac{\text{Volume in mL}}{1000} \]For example, if you have 274 mL of solution, convert this to liters by dividing by 1000:\[ \frac{274 \text{ mL}}{1000} = 0.274 \text{ L} \]This means 274 milliliters is 0.274 liters.

Molarity Formula

Molarity (M) is a measure of the concentration of a solution, specifically the number of moles of solute per liter of solution. The formula for molarity is:\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]To find the molarity of a KCl solution with 0.209 moles of KCl in 0.274 liters of solution:\[ M = \frac{0.209 \text{ mol}}{0.274 \text{ L}}\]After performing the division, you'll find:\[ M = 0.763 \text{ M} \]So, the molarity of the KCl solution is 0.763 M. This measure tells you the concentration of KCl in the solution.